Triangle Solver Calculator

Solve any triangle using sides and angles. Supports SSS, SAS, ASA, AAS, SSA cases. Calculate missing dimensions, area, perimeter, heights, and more.

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Triangle Solver

Enter any 3 values (sides or angles) to solve the triangle. Side a is opposite angle A, side b opposite angle B, side c opposite angle C.

Convention: Side a opposite ∠A, side b opposite ∠B, side c opposite ∠C

Side a (opposite ∠A)

Side b (opposite ∠B)

Side c (opposite ∠C)

∠A (degrees)

∠B (degrees)

∠C (degrees)

Triangle Case

How to use:

Enter any 3 known values (sides or angles). The calculator will automatically detect the case and solve for all unknown values. For SAS and ASA, ensure the angle is between the two given sides.

Triangle Solution

Case Detected: N/A

✓ Solvable

Area

Perimeter

Semi-perimeter

Circumradius (R)

Inradius (r)

Complete Triangle Dimensions

Sides

Side a = 0.0000

Side b = 0.0000

Side c = 0.0000

Angles

∠A = 0.00°

∠B = 0.00°

∠C = 0.00°

Sum of angles = 180.00°

Heights & Other Properties

Height from A (hₐ)

Height from B (hբ)

Height from C (h꜀)

Median to a

Median to b

Median to c

Ambiguous Case - Two Possible Solutions

Solution 1 (Acute Triangle)

Side a = 0.0000

∠A = 0.00°

∠B = 0.00°

Area = 0.0000

Solution 2 (Obtuse Triangle)

Side a = 0.0000

∠A = 0.00°

∠B = 0.00°

Area = 0.0000

Calculation Steps & Formulas Used

Step 1: Detecting case from inputs...
Step 2: Applying triangle laws...
Step 3: Calculating missing values...

Triangle Type Identifier

Enter triangle sides or angles to determine the triangle type (scalene, isosceles, equilateral, acute, obtuse, right).

Identification Method

Side a

Side b

Side c

Triangle Formulas Reference

Quick reference for triangle formulas, laws, and solving methods.

Triangle Laws

Law of Sines

a/sin(A) = b/sin(B) = c/sin(C) = 2R

Where R is circumradius

Law of Cosines

a² = b² + c² - 2bc·cos(A)

b² = a² + c² - 2ac·cos(B)
c² = a² + b² - 2ab·cos(C)

Triangle Sum Theorem

A + B + C = 180°

Sum of interior angles

Area Formulas

Base & Height

Area = ½ × base × height

Heron's Formula

Area = √[s(s-a)(s-b)(s-c)]

s = semi-perimeter

Two Sides & Included Angle

Area = ½ ab·sin(C)

= ½ bc·sin(A) = ½ ac·sin(B)

Solving Cases

Case	Given	Method
SSS	3 sides	Law of Cosines
SAS	2 sides & included angle	Law of Cosines, then Law of Sines
ASA	2 angles & included side	Angle sum, then Law of Sines
AAS	2 angles & non-included side	Angle sum, then Law of Sines
SSA	2 sides & non-included angle	Law of Sines (ambiguous case)